Abstract

Of the Lorenz-type instabilities expected in optical systems, the single-mode instability in optical bistability has been the subject of detailed theoretical and experimental work by our groups. A treatment employing the plane-wave and mean-field limits of the Maxwell-Bloch equations predicts a rich variety of higher-order bifurcations including period doublings and intermittency.¹ An extension of this work to include the transverse dependence of the intracavity field reveals no significant qualitative differences between the plane-wave theory and the Gaussian beam theory as regards the stability boundaries obtained from a linearized analysis.² The instability persists in the presence of a Gaussian transverse profile and the boundaries are not radically modified compared with those obtained from the plane-wave theory. However, numerical integration of the Maxwell-Bloch equations in the single transverse mode approximation does not show the wealth of higher-order dynamic states present in the plane-wave case. An experimental investigation of optical bistability for two-level atoms in a single transverse, single longitudinal mode cavity exhibits limit cycle oscillation with stability boundaries that agree well with the boundaries obtained from the work in Ref. ². However, for the range of values C < 300, |Δ| < 5, |θ| < 50, X ~ 10², the experimental results do not show the diversity of higher dynamic states expected from the plane-wave theory, in agreement with our numerical results. In addition the measurements support the existence of a single transverse mode oscillation. The sum of our theoretical and experimental work provides a quantitative statement for the role of the transverse effects in optical instabilities.

© 1986 Optical Society of America